Answer:
initial outlay $40,000
savings per year = $5,200
additional contribution margin = 2,000 x $2.40 = $4,800
machines useful life = 6 years
1) total annual cash flows (assuming no residual value)
Year₀ = -$40,000
Year₁ = $5,200 + $4,800 = $10,000
Year₂ = $10,000
Year₃ = $10,000
Year₄ = $10,000
Year₅ = $10,000
Year₆ = $10,000
2) to determine IRR we can use a financial calculator or the present value of an annuity formula:
PV = annual payment x annuity factor
PV = $40,000
annual payment = $10,000
annuity factor = $40,000 / $10,000 = 4
3) using present value of an annuity table:
we have 6 periods, and we must look for an interest rate that results in an annuity factor of 4 = 13% (the exact annuity factor is 3.998)
using a financial calculator, the IRR = 12.98%, which we can round to 13%
4) the cash flows will be:
Year₀ = -$40,000
Year₁ = $10,000
Year₂ = $10,000
Year₃ = $10,000
Year₄ = $10,000
Year₅ = $10,000
Year₆ = $20,515
We cannot use the annuity formula now because our annuities are not equal. Using a financial calculator, IRR = 16.99%
